Concrete representation of martingales

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Concrete representation of martingales

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/9728

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Title: Concrete representation of martingales
Author: Montgomery-Smith, Stephen, 1963-
Keywords: UMD spaces
Skorohod representation
Lebesgue measure
Date: 2011-01-26
Abstract: Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0,1]n such that ∫01 dn(x1,...,xn) dxn = 0 for almost all x1,...,xn-1, and such that the law of (fn) is the same as the law of (∑k=1n dn(x1,...,xn)). Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker version of a result of McConnell that provides a Skorohod like representation for vector valued martingales.
URI: http://hdl.handle.net/10355/9728

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